Is there any approximation expression of finite sum of exponential taylor series

Question

Is there any approximation expression of below? $$\sum_{i=0}^{n-1}\frac{1}{i!}x^i$$ $n$ is small like 5 or 10.

What i finally like to do is finding $x$ which satisfy $\sum_{i=0}^{n-1}\frac{1}{i!}x^i=a$

Thank you!